1. "Believer-baptists accuse us of baptising unregenerate people, but believer-baptists do it all the time! How can they live with the fact that people fall away?"

This is unfair. What the believer-baptist is saying is that infant-baptists *delieberately* baptise people who are not regenerate.

For an infant baptist, the church kid who chucks in the faith in high school is a true member of the visible church who has betrayed of their ultimate calling. For the believer baptist, the convert who falls away was never a true member of the visible church - their membership was a sham.

2. "Don't call us 'infant baptists", call us 'convenant baptists'".

Seems sneaky to me. Believer-baptists believe in covenants too, and they believe that baptism is a sign of the covenant. They just happen to believe that the covenant is restricted to regenerate believers.

Emotional: Things are not true cause we want them to be true.
Immoral: Why can you sleep better knowing *your* kid won't go to Hell, but don't care two hoots about the child of the non-Christian?
Illogical: It does not necessarily follow that belief in infant baptism means belief in salvation of your kid.

4. "Baptism is God's promise.... we raise our kids in faith not in fear"

Belief in infant baptism does not mean belief that your kid will go to heaven. Clearly many kids from Christian families fall away from the faith and *don't* go to heaven. So there is some fear, isn't there? And if kids from Christian families don't go to heaven, what do we make of God's alleged 'promise'?

We need far more clarity here. I would prefer to remove these vaguely worded promises altogether. But for the sake of clarity let's map out three possible infant-baptist views:

Presumptive regeneration: Baptism is a sign of God's promise of regeneration and eternal salvation. We presume that all children of Christians are regenerate and predestined. We know that in the mystery of God's will some are not, but our default position, and expectation, is that they are. (I don't like this view, but it is the one where is 'faith not fear' sort of logic works best)
Sign of external blessings: Baptism is a sign only of the external blessings of belonging to the visible church and hearing the gospel, nothing more. Baptism, then says nothing about the salvation of the individual.
Sign of internal and external blessings: Baptism is a sign of God's promise of regeneration and eternal salvation. But we do not give it to children of Christians because we presume they have received the reality. Rather, we consider that it is fitting to give them the sign of regeneration, even though they aren't necessarily regenerate.

5. "Household baptisms in Acts."

Whatever.

6. "We believe in the unity of the covenants."

So does a believer baptist. We both believe that there are some points of discontinuity. The believer baptist just draws the line at a slightly different point.

A strength of Reformed theology is that it is integrated and it joins the dots between its various doctrines really well. The problem is that as a result, Reformed theologians can often argue that every peculiar Reformed doctrine is central and fundamental to the gospel itself. I once read an article that said that Amillenialism, paedobaptism, presbyterian government and limited atonement were all totally central to the gospel and to deny any of them was to let the gospel itself crash down in a heap.